Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22554032 | C2 | semidirect |
| 2. D4×Dic262 | C2 | semidirect |
| 3. #22553670 | C2 | semidirect |
| 4. #22553663 | C2 | semidirect |
| 5. #22553606 | C2 | semidirect |
| 6. #22553592 | C2 | semidirect |
| 8. #22553517 | C2 | semidirect |
| 9. #22553442 | C2 | semidirect |
| 10. #22553409 | C2 | semidirect |
| 122. C131 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554032 | 2 |
| D4×Dic262 | 2 |
| #22553670 | 2 |
| #22553663 | 2 |
| #22553606 | 2 |
| #22553592 | 2 |
| #22553525 | 2 |
| #22553517 | 2 |
| #22553442 | 2 |
| #22553409 | 2 |
| C4×D8×C131 | 2 |
| #3367 | 131 |